A closed Ricci flow with bounded scalar curvature and finite-time curvature blowup

Abstract

We disprove the scalar-curvature extension conjecture in its unrestricted all-dimensions form. In sufficiently high dimension, we construct a Ricci flow on a closed manifold whose scalar curvature remains uniformly bounded while full curvature diverges at a finite maximal time. In one fixed sufficiently high dimension, the examples have two-sided power-law curvature blowup with arbitrarily large exponents.